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Introduction to Proof-based Discrete Mathematics

Program(s): Immersion

This course is currently at capacity for students applying in the Extended round. We are admitting students to the waitlist only, and students who currently are on the waitlist will be given priority if places become available.

This course will introduce you to higher-level mathematical argumentation and proof, an understanding of which is crucial to making the transition from high school to undergraduate math coursework. What we take as given early on in the study of mathematics actually has reasoning behind it, and this course will show you how to begin to uncover and articulate that reasoning for yourself. To do so, we will focus on the seemingly simple question, “How do we count?”  Answering this question will require thinking in terms of sets rather than numbers, so we will begin with naïve (as opposed to axiomatic) set theory and basic set operations, then see how these operations correspond to counting problems including infinite sets. We will also consider topics such as paradoxes of infinity, countability and uncountability, and advanced theories about counting. On a daily basis, students will attend lectures, work in small groups, and present their mathematical arguments and findings in a mutually supportive, inclusive, and welcoming space.

See sample syllabus here.

Remote or Residential

✓ Residential (On-Campus)


Course Considerations

Students must have completed Geometry, Algebra 1, and Algebra 2 to apply.

Math Intensive

Course Overview

Start Date

July 10

End Date

July 26

Current Grade / Education Level

9th Grade
10th Grade
11th Grade



Class Details

Course Code

MATH 10301 94

Class Day(s)

Mon Tues Wed Thurs Fri

Class Duration (CST)


3:00 P.M.


Session II

Course Length

3 weeks

HS Orientation Date

July 08
July 09

Primary Instructor

Matthew Gelvin

Academic Interest

Math and Computer Science